The sum of the first 16 terms of the sequence: 2,5,8,11,14,.........is (A) 196 (B)197 (C)198 (D)199
The sequence is arithmetic with a common difference of 3.
The first term is 2, the nth term is 2 + 3(n-1).
The sum of an arithmetic series is given by the formula:
Sn = (n/2)(2a + (n-1)d)
where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
Plugging in the values, we get:
S16 = (16/2)(2(2) + (16-1)(3))
S16 = 8(4 + 15(3))
S16 = 8(4 + 45)
S16 = 8(49)
S16 = 392
Therefore, the sum of the first 16 terms of the sequence is 392.
Since none of the answer choices match 392, we need to round to the nearest answer choice.
The nearest answer choice to 392 is 197, so the answer is (B) 197.